We present two families of analytical solutions of the one-dimensional nonlinear Schrödinger equation, which describe the dynamics of bright and dark solitons in Bose-Einstein condensates (BECs) with the time-dependent interatomic interaction in an expulsive parabolic and complex potential. We also demonstrate that the lifetime of both a bright soliton and a dark soliton in BECs can be extended by reducing both the ratio of the axial oscillation frequency to radial oscillation frequency and the loss of atoms. It is interesting that a train of bright solitons may be excited with a strong enough background. An experimental protocol is further designed for observing this phenomenon.

It is demonstrated that rotating waveguide eigenmodes may exert a longitudinal force, positive or negative, as well as a torque on the guiding structure itself or part of it. Configurations that are considered include a lossy dielectric cylinder bounded by a hollow waveguide, and a lossy dielectric fiber. Both propagating and evanescent eigenmodes are considered. The analysis is based on a general formulation of the linear and angular momentum currents flowing in the waveguide. The results of this study suggest a novel type of light-driven machine.

We have performed a theoretical analysis of the photon-echo-based quantum memory realized recently in A. L. Alexander et al., Phys. Rev. Lett. 96, 043602 (2006) in the medium with linear correlation between atomic spatial coordinates and frequency detunings of the inhomogeneously broadened transition. A more general vision on the physical picture of temporal and spatial light-atoms dynamics has been obtained in the analytical solutions, taking into account the atomic phase relaxation, inhomogeneous broadening, and arbitrary parameters of the probe light pulses. We have evaluated preferable experimental conditions for the storage of incoming data light field modes where quantum memory efficiency and fidelity have been found. Physics of high efficiency in the forward geometry of the quantum memory and advantages for the realization of more universal long-lived storage on this basis are clarified.

In two-dimensional (2D) photonic crystals (PC’s), we demonstrate compact optical waveguide isolators in which light can propagate only one way. Waveguides are composed of magneto-optical materials with magnetic domain walls. Magneto-optical effects and magnetic domain walls break time-reversal and space-inversion symmetries, respectively, leading to nonreciprocal waveguides with different group velocities for forward and backward propagating light of a given frequency. When backward light has a zero group velocity, only forward light can be transmitted while backward light stops. Slow leakage of backward light (when the group velocity is not precisely zero) is eliminated by introducing absorption loss in nonreciprocal PC waveguides. Then, absorption of forward light is less than that of backward light. Introducing gain material and signal amplification by current injection, forward light can propagate with no net loss and only backward light is attenuated. We demonstrate that backward light, with nearly zero group velocity, can be eliminated because of absorption over a long effective optical path length. This enables compact on-chip photonic band-gap isolators. The waveguide isolator is assumed to be composed of europium oxide with the Faraday rotation angle of ${\theta }_F=3.49\times {10}^3\mathrm{rad}∕\mathrm{cm}$ at wavelength $\lambda =1.5\mu \mathrm{m}$ under a magnetic field $0.9\text{Tesla}$. In a waveguide isolator with the length of $8.5\mu \mathrm{m}$, transmittance of backward light is mostly zero at a specific frequency when transmittance of forward light is amplified to 1 by current injection. The usable bandwidth is up to $12\mathrm{nm}$ centered at $1.5\text{micron}$ wavelength as the device length is increased $(L=42.6\mu \mathrm{m})$. We demonstrate similar results for an asymmetric nonreciprocal waveguide without a magnetic domain wall. The possibility of compact on-chip photonic band-gap isolators is demonstrated for 2D membrane photonic crystals with finite thickness in the third dimension. Computations are performed using plane wave expansion, finite difference time domain, and optical Wannier function methods.

We discuss a general model of a quantum memory for a single light mode in a collective mode of atomic oscillators. The model includes interaction Hamiltonians that are of second order in the canonical position and momentum operators of the light and atomic oscillator modes. We also consider the possibility of measurement and feedback. We identify an interaction Hamiltonian that leads to an ideal mapping by pure unitary evolution and compare several schemes which realize this mapping using a common continuous-variable description. In particular, we discuss schemes based on the off-resonant Faraday effect supplemented by measurement and feedback and proper preparation of the atoms in a squeezed state and schemes based on off-resonant Raman coupling as well as electromagnetically induced transparency.

This paper discusses a combination of atomic and molecular transition frequencies that makes it possible to measure the variance in the proton-to-electron mass ratio $\beta$ with high sensitivity. We consider the combination of two atomic transition frequencies $f(A,B)$ and one molecular vibrational transition $f$ (mol). When $f_p=f\left(A\right)-f\left(B\right)-f$ (mol) is much lower than $f$ (mol), $f_p$ is much more sensitive to the variance in $\beta$ than $f$ (mol).

Recently, a genuine four-qubit entangled state ${\mid {\chi }^{00}⟩}_{3214}$ has been proposed [Y. Yeo and W. K. Chua, Phys. Rev. Lett. 96, 060502 (2006)]. This state has many interesting entanglement properties and possible applications in quantum information processing and fundamental tests of quantum physics. Here we present a simple scheme for generating such a state in an ion-trap system. We also demonstrate how to discriminate between the 16 basis states $\{{\mid {\chi }^{ij}⟩}_{3214}={\sigma }_3^i{\sigma }_1^j{\mid {\chi }^{00}⟩}_{3214},i,j=0,1,2,3\}$.

Instances of discrete states coupled to continua are physically ubiquitous. Numerical simulations of such systems often rely on a discrete representation of the continuum by a large but finite set of discrete levels, or “pseudostates.” In this paper, we develop a method based on the prior work of Kazansky to derive an efficient discrete representation of an arbitrary continuum. For several test cases, our method allows the simulation of non-Markovian decay dynamics with a far smaller set of pseudostates than previously required. We also discuss how this approach can be viewed as a “complex scaling” of the band energy coordinate.

Temporary negative-ion formation has been investigated by observing photon emission from electron-impact-excited $4s4p{{}^{3}P}_1$, $4s4p{{}^{1}P}_1$, $4s4d{{}^{3}D}_{1,2,3}$, $4s4d{{}^{1}D}_2$, and $4s5d{{}^{3}D}_{1,2,3}$ states of zinc. Photon excitation functions are presented for incident electron energies from the first excited state threshold (4.003 eV) to the first ionization potential (9.394 eV). The energies of isolated negative-ion resonance structures have been determined by fitting Fano profiles. These energies, and those of key features in the complicated overlapping resonance profiles, are compared with theory and previous experiments. The strength of resonance contributions, and which structures are dominant, depends on the spin and orbital angular momentum properties of the observed state.

We carry out ab initio study of a ground state phase diagram of spin-$1∕2$ cold fermionic atoms within a twofold degenerate $p$ band of an anisotropic optical lattice. Using the Gutzwiller variational approach, we show that a robust ferromagnetic phase exists for a vast range of band fillings and interacting strengths. The ground state crosses over from a spin density wave state to a spin-1 Neel state at half filling. An additional harmonic trap will induce spatial separation of various phases. We also discuss several relevant observable consequences and detection methods. An experimental test of the results reported here may shed some light on the long-standing issue of itinerant ferromagnetism.

We evaluate the extraction of angular momentum from quantized vortices in trapped Bose-Einstein condensates. Within a variational approach we show that the energy barrier between the ground state and the state containing an axisymmetric vortex can be crossed in a scattering process by density perturbations. The transfer of angular momentum can be made total for suitably chosen density perturbations carrying about 10% of the ground-state energy, irrespectively of the number of particles in the condensate. A similar pattern is reproduced by the full solution of the Gross-Pitaevskii equation, although interference and diffusion effects are now seen to limit the efficiency of the process.

Total photoionization cross sections of doubly excited He have been measured up to the single ionization threshold $I_{15}$ of ${\mathrm{He}}^{+}$ and calculated up to $I_{17}$ revealing excellent agreement. The fact that all spectra are dominated by principal Rydberg series is explained by the observation that the quantity $F=N-K$, representing angular motion, is an approximate quantum number for a large fraction of states. While the nearest-neighbor energy spacings between resonances of Rydberg series with small $F$ approach a Wigner distribution, reflecting chaos in radial motion, there is no indication for a transition to full chaos including angular motion.

The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation value. In contrast to the previous numerical examinations, our discussion presents an exact calculation for the determination of the geometric phase. Through two representative examples, our calculation shows the intimate connection between the geometric phase and phase transition: different behaviors of the geometric phase can be identified in this paper, which are directly related to the energy gap above the ground state.

We construct a scheme for the preparation, pairwise entanglement via exchange interaction, manipulation, and measurement of individual group-II-like neutral atoms (Yb, Sr, etc.). Group-II-like atoms proffer important advantages over alkali metals, including long-lived optical-transition qubits that enable fast manipulation and measurement. Our scheme provides a promising approach for producing weighted graph states, entangled resources for quantum communication, and possible application to fundamental tests of Bell inequalities that close both detection and locality loopholes.

Building on the well-known Unruh-Davies effect, we examine the effects of projective measurements and quantum communications between accelerated and stationary observers. We find that the projective measurement by a uniformly accelerated observer can excite real particles from the vacuum in the inertial frame, even if no additional particles are created by the measurement process in the accelerating frame. Furthermore, we show that the particles created by this accelerating measurement can be highly entangled in the inertial frame, and it is also possible to use this process to generate even maximally entangled two-qubit states by a certain arrangement of measurements. As a by-product of our analysis, we also show that a single qubit of information can be perfectly transmitted from the accelerating observer to the inertial one. In principle, such an effect could be exploited in designing an entangled-state generator for quantum communication.

We propose a hybrid quantum computing scheme where qubit degrees of freedom for computation are combined with quantum continuous variables for communication. In particular, universal two-qubit gates can be implemented deterministically through qubit-qubit communication, mediated by a continuous-variable bus mode (“qubus”), without direct interaction between the qubits and without any measurement of the qubus. The key ingredients are controlled rotations of the qubus and unconditional qubus displacements. The controlled rotations are realizable through typical atom-light interactions in quantum optics. For such interactions, our scheme is universal and works in any regime, including the limits of weak and strong nonlinearities.

All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption whose validity is not obvious. We introduce two different schemes by which any arbitrary time evolution and measurement can be implemented with desired accuracy by using rotationally invariant Hamiltonians that act on the given system and two ancillary systems serving as reference frames. These frames specify the $z$ and $x$ directions and are independent of the desired time evolution. We also investigate the effects of quantum fluctuations that inevitably arise due to usage of a finite system as a reference frame and estimate how fast these fluctuations tend to zero when the size of the reference frame tends to infinity. Moreover, we prove that for a general symmetry any symmetric quantum operation can be implemented just by using symmetric interactions and ancillas in the symmetric states.

We present a general multicomponent density-functional theory in which electrons and nuclei are treated completely quantum mechanically, without the use of a Born-Oppenheimer approximation. The two fundamental quantities in terms of which our theory is formulated are the nuclear $N$-body density and the electron density expressed in coordinates referring to the nuclear framework. For these two densities, coupled Kohn-Sham equations are derived, and the electron-nuclear correlation functional is analyzed in detail. The formalism is tested on the hydrogen molecule ${\mathrm{H}}_2$ and its positive ion $\mathrm{H}_2{}^{+}$, using several approximations for the electron-nuclear correlation functional.

We investigate the possibility of producing ultracold $\mathrm{N}{\mathrm{H}}_3$ molecules by sympathetic cooling in a bath of ultracold atoms. We consider the interactions of $\mathrm{N}{\mathrm{H}}_3$ with alkali-metal and alkaline-earth-metal atoms, and with Xe, using ab initio coupled-cluster calculations. For $\mathrm{Rb}\text{−}\mathrm{N}{\mathrm{H}}_3$ and $\mathrm{Xe}\text{−}\mathrm{N}{\mathrm{H}}_3$ we develop full potential energy surfaces, while for the other systems we characterize the stationary points (global and local minima and saddle points). We also calculate isotropic and anisotropic van der Waals $C_6$ coefficients for all the systems. The potential energy surfaces for interaction of $\mathrm{N}{\mathrm{H}}_3$ with alkali-metal and alkaline-earth-metal atoms all show deep potential wells and strong anisotropies. The well depths vary from $887{\mathrm{cm}}^{-1}$ for $\mathrm{Mg}\text{−}\mathrm{N}{\mathrm{H}}_3$ to $5104{\mathrm{cm}}^{-1}$ for $\mathrm{Li}\text{−}\mathrm{N}{\mathrm{H}}_3$. This suggests that all these systems will exhibit strong inelasticity whenever inelastic collisions are energetically allowed and that sympathetic cooling will work only when both the atoms and the molecules are already in their lowest internal states. $\mathrm{Xe}\text{−}\mathrm{N}{\mathrm{H}}_3$ is more weakly bound and less anisotropic.

We discuss the precession of spin-polarized ultracold neutrons (UCNs) and ${}^3\mathrm{He}$ atoms in uniform and static magnetic and electric fields and calculate the spin relaxation effects from motional $\mathbf{v}\times \mathbf{E}$ magnetic fields. Particle motion in an electric field creates a motional $\mathbf{v}\times \mathbf{E}$ magnetic field, which when combined with collisions produces variations of the total magnetic field and results in spin relaxation of neutron and ${}^3\mathrm{He}$ samples. The spin relaxation times $T_1$ (longitudinal) and $T_2$ (transverse) of spin-polarized UCNs and ${}^3\mathrm{He}$ atoms are important considerations in a new search for the neutron electric dipole moment at the Spallation Neutron Source $n\mathrm{EDM}$ experiment. We use a Monte Carlo approach to simulate the relaxation of spins due to the motional $\mathbf{v}\times \mathbf{E}$ field for UCNs and for ${}^3\mathrm{He}$ atoms at temperatures below $600\mathrm{mK}$. We find the relaxation times for the neutron due to the $\mathbf{v}\times \mathbf{E}$ effect to be long compared to the neutron lifetime, while the ${}^3\mathrm{He}$ relaxation times may be important for the $n\mathrm{EDM}$ experiment.